If i(t) = 4 sin 2t + 3t, find i(t) when t = pi/3 and when t = 0.6 rad.

Substitute $t = \frac{\pi}{3}$ into the function:

$$i\left(\frac{\pi}{3}\right) = 4 \sin\left(2 \cdot \frac{\pi}{3}\right) + 3 \cdot \frac{\pi}{3}$$ $$i\left(\frac{\pi}{3}\right) = 4 \sin\left(\frac{2\pi}{3}\right) + \pi$$

We know that $\sin\left(\frac{2\pi}{3}\right) = \sin\left(\pi - \frac{\pi}{3}\right) = \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$.

$$i\left(\frac{\pi}{3}\right) = 4 \left(\frac{\sqrt{3}}{2}\right) + \pi$$ $$i\left(\frac{\pi}{3}\right) = 2\sqrt{3} + \pi$$

Now, calculate the numerical value:

$$i\left(\frac{\pi}{3}\right) \approx 2(1.73205) + 3.14159$$ $$i\left(\frac{\pi}{3}\right) \approx 3.46410 + 3.14159$$ $$i\left(\frac{\pi}{3}\right) \approx \boxed{6.6057}$$

Substitute $t = 0.6$ into the function:

$$i(0.6) = 4 \sin(2 \cdot 0.6) + 3 \cdot 0.6$$ $$i(0.6) = 4 \sin(1.2) + 1.8$$

Using a calculator (ensure it's in radian mode):

$$\sin(1.2) \approx 0.932039$$ $$i(0.6) \approx 4(0.932039) + 1.8$$ $$i(0.6) \approx 3.728156 + 1.8$$ $$i(0.6) \approx \boxed{5.5282}$$